Final answer:
The coordinates that divide the line segment PQ in the ratio of 5:3 are calculated using the section formula, resulting in the point (2, 2). This point wasn't among the provided options, indicating a possible error in the question or options given.
Step-by-step explanation:
The student is asking to find the coordinates of a point that divides the line segment PQ in the ratio of 5:3. To do this, we use the formula for a point that divides a line segment into a given ratio, which is known as the section formula.
The section formula in two dimensions for a line segment with endpoints (x1, y1) and (x2, y2) and a ratio m:n is given by:
((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))
Given points P(-8, 7) and Q(8, -1) and the ratio 5:3, we substitute these values into the formula to find the coordinates. This results in:
((5(8) + 3(-8)) / (5 + 3), (5(-1) + 3(7)) / (5 + 3))
= (40 - 24) / 8, (-5 + 21) / 8
= (16 / 8, 16 / 8)
= (2, 2)
Therefore, the coordinates that divide the line segment PQ in the ratio of 5:3 are (2, 2), which is not among the options provided in the question.